Should I apply for a BRP under TOC as a Tier-4?

hi all I would really appreciate some info on this
I applied for a Tier-4 general student visa overseas before the BRP system was introduced. My application was around July 13th 2015 and I received my visa as a sticker on my passport on July 31st. my passport was renewed in June 2016 and I had no trouble traveling as long as I had both passports on me.
I have started applying for full time jobs as I reached the end of my Masters and I want to secure a job under tier-2 before my current leave runs out ( February 2017).
My question is, do I even need to transfer the remaining leave onto a BRP and post my passports even before I apply or get a confirmed offer of sponsorship? Will the employer offering me a job retract the offer if they find out my Tier-4 visa is on an old passport and that I haven't applied for a BRP under TOC yet?
I don't know how long it takes to get back the passports and BRP so I am worried about posting it to Durham if it is going to take more than 2 months. If someone has had a similar experience to this, please share it you'd really be helping me out
thank you for reading this.
PS- I do have the printed TOC form, passports and other evidence but didn't want to mail it until I got a response here
Adding another point - I've been working part-time for the last year since I came here